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1.
A nonsmooth version of Newton's method   总被引:68,自引:0,他引:68  
Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian forC 2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.This author's work is supported in part by the Australian Research Council.This author's work is supported in part by the National Science Foundation under grant DDM-8721709.  相似文献
2.
Global Convergence of Conjugate Gradient Methods without Line Search   总被引:11,自引:0,他引:11  
Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: (1) The Fletcher–Reeves method, the Hestenes–Stiefel method, and the Dai–Yuan method applied to a strongly convex LC 1 objective function; (2) The Polak–Ribière method and the Conjugate Descent method applied to a general, not necessarily convex, LC 1 objective function.  相似文献
3.
A trust region algorithm for minimization of locally Lipschitzian functions   总被引:7,自引:0,他引:7  
The classical trust region algorithm for smooth nonlinear programs is extended to the nonsmooth case where the objective function is only locally Lipschitzian. At each iteration, an objective function that carries both first and second order information is minimized over a trust region. The term that carries the first order information is an iteration function that may not explicitly depend on subgradients or directional derivatives. We prove that the algorithm is globally convergent. This convergence result extends the result of Powell for minimization of smooth functions, the result of Yuan for minimization of composite convex functions, and the result of Dennis, Li and Tapia for minimization of regular functions. In addition, compared with the recent model of Pang, Han and Rangaraj for minimization of locally Lipschitzian functions using a line search, this algorithm has the same convergence property without assuming positive definiteness and uniform boundedness of the second order term. Applications of the algorithm to various nonsmooth optimization problems are discussed.This author's work was supported in part by the Australian Research Council.This author's work was carried out while he was visiting the Department of Applied Mathematics at the University of New South Wales.  相似文献
4.
We study a variational inequality problem VI(X,F) with X being defined by infinitely many inequality constraints and F being a pseudomonotone function. It is shown that such problem can be reduced to a problem of finding a feasible point in a convex set defined by infinitely many constraints. An analytic center based cutting plane algorithm is proposed for solving the reduced problem. Under proper assumptions, the proposed algorithm finds an -optimal solution in O*(n 2/2) iterations, where O*(·) represents the leading order, n is the dimension of X, is a user-specified tolerance, and is the radius of a ball contained in the -solution set of VI(X,F).  相似文献
5.
Multistage stochastic linear programming (MSLP) is a powerful tool for making decisions under uncertainty. A deterministic equivalent problem of MSLP is a large-scale linear program with nonanticipativity constraints. Recently developed infeasible interior point methods are used to solve the resulting linear program. Technical problems arising from this approach include rank reduction and computation of search directions. The sparsity of the nonanticipativity constraints and the special structure of the problem are exploited by the interior point method. Preliminary numerical results are reported. The study shows that, by combining the infeasible interior point methods and specific decomposition techniques, it is possible to greatly improve the computability of multistage stochastic linear programs.  相似文献
6.
一类反应扩散方程奇摄动Robin问题的广义解   总被引:1,自引:0,他引:1  
讨论了一类奇摄动反应扩散方程R ob in问题.在适当的条件下,研究了问题广义解的渐近性态.  相似文献
7.
The relationship between the mathematical program with linear complementarity constraints (MPLCC) and its inequality relaxation is studied. Based on this relationship, a new sequential quadratic programming (SQP) method is presented for solving the MPLCC. A certain SQP technique is introduced to deal with the possible infeasibility of quadratic programming subproblems. Global convergence results are derived without assuming the linear independence constraint qualification for MPEC, the nondegeneracy condition, and any feasibility condition of the quadratic programming subproblems. Preliminary numerical results are reported. Research is partially supported by Singapore-MIT Alliance and School of Business, National University of Singapore.  相似文献
8.
基于模糊理论的闭环供应链定价决策研究   总被引:1,自引:0,他引:1  
考虑一个单周期二级模糊闭环供应链系统.模糊性存在于制造过程、再制造过程、需求过程和回收过程.利用模糊理论和博弈论理论等知识,分别在集中式和分散式决策方式下给出了制造商和零售商的最优定价决策,以及分散决策方式下的系统协调策略,并且利用数值算例对所得结果进行了分析.  相似文献
9.
In this paper we propose the finite difference method for the forward-backward heatequation.We use a coarse-mesh second-order central difference scheme at the middleline mesh points and derive the error estimate.Then we discuss the iterative methodbased on the domain decomposition for our scheme and derive the bounds for the rates ofconvergence.Finally we present some numerical experiments to support our analysis.  相似文献
10.
Consider the problem of computing the smallest enclosing ball of a set of m balls in n. Existing algorithms are known to be inefficient when n > 30. In this paper we develop two algorithms that are particularly suitable for problems where n is large. The first algorithm is based on log-exponential aggregation of the maximum function and reduces the problem into an unconstrained convex program. The second algorithm is based on a second-order cone programming formulation, with special structures taken into consideration. Our computational experiments show that both methods are efficient for large problems, with the product mn on the order of 107. Using the first algorithm, we are able to solve problems with n = 100 and m = 512,000 in about 1 hour.His work was supported by Australian Research Council.Research supported in part by the Singapore-MIT Alliance.  相似文献
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